$($Future value of a complex annuity$)$ Springfield mogul Montgomery Burns, age $90,$ wants to retire at age $100$ so he can steal candy from babies full time. Once Mr$.$ Burns retires, he wants to withdraw

$$0\mathrm{.}9$ billion at the beginning of each year for $9$ years from a special offshore account that will pay $22$ percent annually. In order to fund his retirement, Mr$.$ Burns will make $10$ equal end$-$of$-$the$-$year deposits

in this same special account that will pay $22$ percent annually. a$.$ How much money will Mr$.$ Burns need at age $100,$ b$.$ and how large of an annual deposit must he make to fund this retirement account?